The try scoring bonus point sees South Africa qualify for the semi finals where they will take on Argentina while England fail to reach the final four for the first time.
England, who featured the Gloucester Rugby trio of Koree Britton, Ryan Mills and Dan Robson, looked the superior side in the first half but failed to make the most of their supremacy.
They played a tight, controlled game and only had a Tommy Bell penalty to show for their efforts with Bath's Tom Heathcote missing two other attempts.
And it came back to bite them as William Small-Smith pounced just a couple of minutes into the second half. His try and the subsequent conversion gave South Africa a lead they would never relinquish.
Another Bell penalty made it 7-6 but the South African back row seized control of the game as England's previously watertight defence started to fall apart.
The excellent Shaun Adendorff scored the first of his two tries and, although Bell got it back to 14-12 with two further penalties, it was as close as England got.
Openside Pieter Steph du Toit added a third try and Adendorff's second clinched the bonus point.
England threw caution to the wind as they strove to fight back and Bell slotted a fifth penalty but over-ambition saw errors aplenty and they never really got close to crossing the South Africa line.
England looked stunned as the final whistle blew as the failure to make the semi finals sank home.